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MEP 2006, 7-11 November 2006, Guanajuato, Guanajuato, México. 150. FRESNEL ELLIPSOIDS, REFLECTION, REFRACTION AND. SCATTERING IN A ...
MEP 2006, 7-11 November 2006, Guanajuato, Guanajuato, México.

FRESNEL ELLIPSOIDS, REFLECTION, REFRACTION AND SCATTERING IN A TELECOMMUNICATION NETWORK DESIGN M. Tecpoyotl-Torres1, H. García-Tapia1, R. Pelanis,1 O. G. Ibarra-Manzano and J. SánchezMondragón2 1

Research Centre of Engineering and Applied Sciences (CIICAp) Autonomous State University of Morelos (UAEM), 62209, Av. Universidad No 1001, Cuernavaca, Mor., Mexico, e-mail: [email protected] Phone: 2-777-3297084, Fax: 2-777-3297084, e-mail: [email protected] 2 National Institute for Astrophysics, Optics, and Optics (INAOE) 72000, Luis Enrique Erro #1, Tonantzintla, Pue. Mexico Phone: 2-222-2472011, e-mail: [email protected] Abstract-We present the relevant considerations taken into account in the reorganization and growth of the telecommunication network of the Autonomous University of Morelos (UAEM), Mexico, in order to obtain an optimal performance, such as the analysis of Fresnel Ellipsoids, the route profiles and the broadband growth. This reorganization is due to the need of a higher information transfer rate and a wider broadband, to be supported on a wireless platform. The aim is to have a private network for video, voice and data transmission using the Internet Protocol (IP), which is a data-oriented protocol used for communicating data across a packet switched network. The characteristics of the terrain allows us a detailed analysis of the reflections produced by the surface profile. The influence of the weather and the environment is also considered in the design. Keywords: Broad band, wireless links, multiple path, antennas.

INTRODUCTION For the design of this network we have considered, on each site, the analysis of the microwave communication elements such as the : radiofrequency (RF) equipment, the antennas and the propagation media. We describe the last one.

Figure 1. Network before the re-organization and increasing with widebands of 128 kbps, except South and East Campus.

Figure 2. Wireless network of the UAEM with wideband from16 Mbps and 24 Mbps.

The design is based on the application of physical concepts such is the reflection, refraction, scattering and the Fresnel Ellipsoids. The information on the physical data on each site, such as the terrain data and the obstacles, were used in the software PATHLOSS for the trajectory analysis of each point in the network. This analysis includes the Fresnel Ellipsoids and its effects on the propagation and on the main signal. In figure 1, we show the previous 1-4244-0628-5/06/$20.00 ©2006 IEEE

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configuration and in figure 2, the current telecommunication network, respectively. The network operates at 5.875 GHz, because this frequency is not discharged and has low traffic. The central part of the UAEM is located at Chamilpa and it is a repeater for six points. The site located at Tres Cumbres is also used as repeater due to its height of the three sites. All the sites are point-to-point links.

FRESNEL ELLIPSOIDS The importance of the Fresnel ellipsoids is due to the attenuation between two antennas, on the presence of non refractive obstacles. Unless there are no obstacles in the first Fresnel Ellipsoid, this could be as large as the vacuum attenuation,. Under these conditions, we know that Transmitter (T) and Receiver (R) have line sight. Considering a one-directional link (figure 1) operating at a frequency f (inversely proportional to λ, at the vacuum), the nthFesnel Ellipsoid is defined by equation (1): λ 2 z (d − z) or (1) z2 + r2 + (d − z ) + r2 − d = n r=± n λ 2

d

The radius of the nth-Fresnel Ellipsoid, considering z=d/2, is given by r1m = λ d / 4 . We have used

P

r

0 T

Z

R z d

Figure 3: Scheme used to define the Fresnel Ellipsoid.

r1m = (1/ 2) 0.3d / f , [1], with m as the unit of the radio and distance; and GHz for f. In figure 4, we show the first and the fourth Fresnel ellipsoids. After its trace, it is necessary to adjust the antenna height in order to maintain clear to the first Fresnel ellipsoid.

1st ellipsoid

4th ellipsoid

Figure 4: First and Fourth Fresnel ellipsoids for the link between Chamilpa and South Campus, the radios are 23.67 m and 47.64 m, respectively.

Figure 5: Effect of trees and buildings. The height of trees is 12 m and of the building is of 40 m at 7.11 km from the first antenna.

REFRACTIONS With the atmosphere presence, the refraction index changes with the altitude, and modifies the beam trajectory, which tends to be curved, according to the changes in the refraction index. An useful approximation for the low troposphere, where the signal propagation between microwave links are carried out, is to assume that the curvature of the beam trajectory is

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equivalent to an straight line trajectory of the beam on the spherical Earth surface with an equivalent radio r=ker0, where r0 is the Earth radio (approx. 6370 km) and ke=1/(1-(r0/ n0)Δn). To assure a beam without obstructions, it is common to use ke=4/3, in order to keep clear the first Fresnel Ellipsoid (see figure 4).

REFLECTIONS (MULTIPATH) The multipath effect helps us to determine the route reflective characteristics as well as other aspects of the propagation conditions. This phenomenon occurs regularly at night, at the first hours of the morning, at midday or during intense rain periods. The multipath effect changes our signal abruptly, and could invert it or have its phase increased, when the effects are quite dense it can be similar to a mirror or specular point. The holding back of the signal energy produces interference over other reception signals or may caused their full canceling out. When it is generated at the beginning of the link, it causes a lower interference, and it can be immediately eliminated, as can be seen in figure 6. Other type of obstruction may be trees and buildings, but for the case considered in figure 5, it was not relevant.

Figure 6. A specular point.

Figure 7: Difraction loss

DIFFRACTION On a route with obstructions we have propagation with diffraction, when this mechanism is dominant; the propagation over the obstacles is assured. The computation of the attenuation caused by real obstacles is modeled using two basic prototypes: one of infinity length (normal to the propagation direction), without considering its width (knife edge), and another one that is basically a cylinder of finite with a constant curvature and a rounded top. It is also possible consider finite dimensions (figure 7). The losses by obstacles may be minimized, the propagation on the same route is due only to the diffraction over the Earth surface, as can be seen in figure 8.

(a)

(b)

Figure 8: Multipath without small (a) and with pronounced obstacles (b).

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ATTENUATION For microwave links, the atmospheric attenuation is minimal for the range from 1 GHz up to 10 GHz. After 2 GHz, it is enough to consider the attenuation by intense rain, because it is responsible for the absorption, scattering and changes in the polarization of the radiowaves.

CONCLUSIONS We analyze the effect of several factors, that impact on the design of microwave links. The availability of the network depends of the design considerations, and it is given in annual percentage, which is traduced in minutes. The time out of service must be the shortest due to the climatic conditions en each link point.

ACKNOWLEDGEMENTS To the UAEM for the implementation of this network. H. García-Tapia also wants to thank to CONACYT-Mexico for his graduate scholarship.

REFERENCES 39. C. Salema. Microwave radio links. Wiley-Interscience 2003, p. 25.

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